2014, 11(6): 1337-1356. doi: 10.3934/mbe.2014.11.1337

Modeling the impact of twitter on influenza epidemics

1. 

Department of Mathematics and Computational Science, University of South Carolina Beaufort, Bluffton, SC 29909, United States

2. 

Department of Communication, University of Connecticut, Storrs, CT 06269, United States

3. 

Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309

Received  December 2013 Revised  June 2014 Published  September 2014

Influenza remains a serious public-health problem worldwide. The rising popularity and scale of social networking sites such as Twitter may play an important role in detecting, affecting, and predicting influenza epidemics. In this paper, we develop a simple mathematical model including the dynamics of ``tweets'' --- short, 140-character Twitter messages that may enhance the awareness of disease, change individual's behavior, and reduce the transmission of disease among a population during an influenza season. We analyze the model by deriving the basic reproductive number and proving the stability of the steady states. A Hopf bifurcation occurs when a threshold curve is crossed, which suggests the possibility of multiple outbreaks of influenza. We also perform numerical simulations, conduct sensitivity test on a few parameters related to tweets, and compare modeling predictions with surveillance data of influenza-like illness reported cases and the percentage of tweets self-reporting flu during the 2009 H1N1 flu outbreak in England and Wales. These results show that social media programs like Twitter may serve as a good indicator of seasonal influenza epidemics and influence the emergence and spread of the disease.
Citation: Kasia A. Pawelek, Anne Oeldorf-Hirsch, Libin Rong. Modeling the impact of twitter on influenza epidemics. Mathematical Biosciences & Engineering, 2014, 11 (6) : 1337-1356. doi: 10.3934/mbe.2014.11.1337
References:
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[3]

M. Ajelli, S. Merler, A. Pugliese and C. Rizzo, Model predictions and evaluation of possible control strategies for the 2009 A/H1N1v influenza pandemic in Italy,, Epidemiol. Infect., 139 (2011), 68.  doi: 10.1017/S0950268810001317.  Google Scholar

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M. Baguelin, A. J. Hoek, M. Jit, S. Flasche, P. J. White and W. J. Edmunds, Vaccination against pandemic influenza A/H1N1v in England: A real-time economic evaluation,, Vaccine, 28 (2010), 2370.  doi: 10.1016/j.vaccine.2010.01.002.  Google Scholar

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D. Balcan, H. Hu, B. Goncalves, P. Bajardi, C. Poletto, J. J. Ramasco, D. Paolotti, N. Perra, M. Tizzoni, W. V. Broeck, V. Colizza and A. Vespignani, Seasonal transmission potential and activity peaks of the new influenza A(H1N1): A Monte Carlo likelihood analysis based on human mobility,, BMC Medicine, 7 (2009).  doi: 10.1186/1741-7015-7-45.  Google Scholar

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J. Cain, F. Romanelli and B. Fox, Pharmacy, social media, and health: Opportunity for impact,, J. Am. Pharm. Assoc., 50 (2010), 745.   Google Scholar

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C. M. Chew and G. Eysenbach, Pandemics in the age of Twitter: Content analysis of tweets during the 2009 H1N1 outbreak,, PLoS One, 5 (2010).  doi: 10.1371/journal.pone.0014118.  Google Scholar

[10]

J. Cui, Y. Sun and H. Zhu, The impact of media on the control of infectious diseases,, J. Dyn. Differ. Equ., 20 (2008), 31.  doi: 10.1007/s10884-007-9075-0.  Google Scholar

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M. E. Halloran, N. M. Ferguson, S. Eubank, I. M. Longini, Jr., D. A. Cummings, B. Lewis, S. Xu, C. Fraser, A. Vullikanti, T. C. Germann, D. Wagener, R. Beckman, K. Kadau, C. Barrett, C. A. Macken, D. S. Burke and P. Cooley, Modeling targeted layered containment of an influenza pandemic in the United States,, PNAS, 105 (2008), 4639.  doi: 10.1073/pnas.0706849105.  Google Scholar

[21]

N. Heaivilin, B. Gerbert, J. E. Page and J. L. Gibbs, Public health surveillance of dental pain via Twitter,, J. Dent. Res., 90 (2011), 1047.  doi: 10.1177/0022034511415273.  Google Scholar

[22]

H. Hirose and L. Wang, Prediction of infectious disease spread using Twitter: A case of influenza,, The Fifth International Symposium on Parallel Architectures, (2012), 100.  doi: 10.1109/PAAP.2012.23.  Google Scholar

[23]

C. Holt, Emerging technologies: Web 2.0,, Health Information Management Journal, 40 (2011), 33.   Google Scholar

[24]

A. Java, X. Song, T. Finin and B. Tseng, Why we Twitter: Understanding Microblogging Usage and Communities,, in Proceedings of the 9th WebKDD and 1st SNA-KDD 2007 Workshop on Web Mining and Social Network Analysis, (2007), 56.  doi: 10.1145/1348549.1348556.  Google Scholar

[25]

V. Lakshmikantham, S. Leela and A. A. Martynyuk, Stability Analysis of Nonlinear Systems,, Marcel Dekker, (1989).   Google Scholar

[26]

J. P. LaSalle, The Stability of Dynamical Systems,, Regional Conference Series in Applied Mathematics, (1976).   Google Scholar

[27]

B. Y. Lee, S. T. Brown, G. W. Korch, P. C. Cooley, R. K. Zimmerman, W. D. Wheaton, S. M. Zimmer, J. J. Grefenstette, R. R. Bailey, T. M. Assi and D. S. Burke, A computer simulation of vaccine prioritization, allocation, and rationing during the 2009 H1N1 influenza pandemic,, Vaccine, 28 (2010), 4875.  doi: 10.1016/j.vaccine.2010.05.002.  Google Scholar

[28]

S. Leekha, N. L. Zitterkopf, M. J. Espy, T. F. Smith, R. L. Thompson and P. Sampathkumar, Duration of influenza A virus shedding in hospitalized patients and implications for infection control,, Infect. Cont. Hosp. Ep., 28 (2007), 1071.  doi: 10.1086/520101.  Google Scholar

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J. Li, D. Blakeley and R. J. Smith?, The failure of $R_0$,, Computational and Mathematical Methods in Medicine, (2011).  doi: 10.1155/2011/527610.  Google Scholar

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R. Liu, J. Wu and H. Zhu, Media/psychological impact on multiple outbreaks of emerging infectious diseases,, Comput. Math. Methods Med., 8 (2007), 153.  doi: 10.1080/17486700701425870.  Google Scholar

[31]

Y. Liu and J. Cui, The impact of media coverage on the dynamics of infectious disease,, Int. J. Biomath., 1 (2008), 65.  doi: 10.1142/S1793524508000023.  Google Scholar

[32]

I. M. Longini, Jr., M. E. Halloran, A. Nizam and Y. Yang, Containing pandemic influenza with antiviral agents,, Am. J. of Epidemiol., 159 (2004), 623.  doi: 10.1093/aje/kwh092.  Google Scholar

[33]

P. Manfredi, P. D. Posta, A. d'Onofrio, E. Salinelli, F. Centrone, C. Meo and P. Poletti, Optimal vaccination choice, vaccination games, and rational exemption: An appraisal,, Vaccine, 28 (2009), 98.  doi: 10.1016/j.vaccine.2009.09.109.  Google Scholar

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A. Mitchell, T. Rosenstiel and L. Christian, What Facebook and Twitter mean for news,, Pew Research Center's Project for Excellence in Journalism, (2012).   Google Scholar

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L. Odden, Top 10 uses of Twitter,, Online Marketing Blog, (2008).   Google Scholar

[38]

P. Poletti, M. Ajelli and S. Merler, Risk perception and effectiveness of uncoordinated behavioral responses in an emerging epidemic,, Math. Biosci., 238 (2012), 80.  doi: 10.1016/j.mbs.2012.04.003.  Google Scholar

[39]

P. Poletti, B. Caprile, M. Ajelli, A. Pugliese and S. Merler, Spontaneous behavioural changes in response to epidemics,, J. Theoret. Biol., 260 (2009), 31.  doi: 10.1016/j.jtbi.2009.04.029.  Google Scholar

[40]

T. C. Reluga, Game theory of social distancing in response to an epidemic,, PLoS Comput. Biol., 6 (2010).  doi: 10.1371/journal.pcbi.1000793.  Google Scholar

[41]

D. Scanfeld, V. Scanfeld and E. L. Larson, Dissemination of health information through social networks: Twitter and antibiotics,, Am. J. Infect. Control, 38 (2010), 182.  doi: 10.1016/j.ajic.2009.11.004.  Google Scholar

[42]

A. Signorini, A. M. Segre and P. M. Polgreen, The use of Twitter to track levels of disease activity and public concern in the U.S. during the influenza A H1N1 pandemic,, PLoS One, 6 (2011).  doi: 10.1371/journal.pone.0019467.  Google Scholar

[43]

A. Smith and J. Brenner, Twitter use 2012,, Pew Internet and American Life Project, (2012).   Google Scholar

[44]

J. M. Tchuenche, and C. T. Bauch, Dynamics of an infectious disease where media coverage influences transmission,, ISRN Biomathematics, 2012 (2012), 1.  doi: 10.5402/2012/581274.  Google Scholar

[45]

J. M. Tchuenche, N. Dube, C. P. Bhunu, R. J. Smith and C. T. Bauch, The impact of media coverage on the transmission dynamics of human influenza,, BMC Public Health, 11 (2011).   Google Scholar

[46]

V. Tweedle and R. J. Smith, A mathematical model of Bieber Fever: The most infectious disease of our time?,, in Understanding the Dynamics of Emerging and Re-Emerging Infectious Diseases Using Mathematical Models (eds. S. Mushayabasa and C. P. Bhunu), (2012), 157.   Google Scholar

[47]

S. J. Sullivan, A. G. Schneiders, C. W. Cheang, E. Kitto, H. Lee, J. Redhead, S. Ward, O. H. Ahmed and P. R. McCrory, 'What's happening?' A content analysis of concussion-related traffic on Twitter,, Brit. J. Sports Med., 46 (2012), 258.  doi: 10.1136/bjsm.2010.080341.  Google Scholar

[48]

M. Szomszor, P. Kostkova and E. de Quincey, Swineflu: Twitter predicts Swine Flu outbreak in 2009,, in Electronic Healthcare, (2010), 18.  doi: 10.1007/978-3-642-23635-8_3.  Google Scholar

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P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,, Math. Biosci., 180 (2002), 29.  doi: 10.1016/S0025-5564(02)00108-6.  Google Scholar

[51]

J. van Dijck, Tracing Twitter: The rise of a microblogging platform,, Int. J. of Media Cultural Polit., 7 (2012), 333.  doi: 10.1386/macp.7.3.333_1.  Google Scholar

[52]

K. Vance, W. Howe and R. P. Dellavalle, Social Internet sites as a source of public health information,, Dermatol. Clin., 27 (2009), 133.  doi: 10.1016/j.det.2008.11.010.  Google Scholar

[53]

M. Wazny, Using viral marketing in campaigns supporting health promotion,, Proceedings of the 13th World Congress on Public Health, (2012).   Google Scholar

[54]

J. T. Wu, S. Riley, C. Fraser and G. M. Leung, Reducing the impact of the next influenza pandemic using household-based public health interventions,, PLoS Med., 3 (2006).  doi: 10.1371/journal.pmed.0030361.  Google Scholar

show all references

References:
[1]

, , ().   Google Scholar

[2]

H. Achrekar, A. Gandhe, R. Lazarus, S. Yu and B. Liu, Twitter improves seasonal influenza prediction,, HEALTHINF, (2012), 61.   Google Scholar

[3]

M. Ajelli, S. Merler, A. Pugliese and C. Rizzo, Model predictions and evaluation of possible control strategies for the 2009 A/H1N1v influenza pandemic in Italy,, Epidemiol. Infect., 139 (2011), 68.  doi: 10.1017/S0950268810001317.  Google Scholar

[4]

E. Aramaki, S. Maskawa and M. Morita, Twitter catches the flu: Detecting influenza epidemics using Twitter,, Proceedings of the 2011 Conference on Empirical Methods in Natural Language Processing, (2011), 1568.   Google Scholar

[5]

M. Baguelin, A. J. Hoek, M. Jit, S. Flasche, P. J. White and W. J. Edmunds, Vaccination against pandemic influenza A/H1N1v in England: A real-time economic evaluation,, Vaccine, 28 (2010), 2370.  doi: 10.1016/j.vaccine.2010.01.002.  Google Scholar

[6]

D. Balcan, H. Hu, B. Goncalves, P. Bajardi, C. Poletto, J. J. Ramasco, D. Paolotti, N. Perra, M. Tizzoni, W. V. Broeck, V. Colizza and A. Vespignani, Seasonal transmission potential and activity peaks of the new influenza A(H1N1): A Monte Carlo likelihood analysis based on human mobility,, BMC Medicine, 7 (2009).  doi: 10.1186/1741-7015-7-45.  Google Scholar

[7]

J. Cain, F. Romanelli and B. Fox, Pharmacy, social media, and health: Opportunity for impact,, J. Am. Pharm. Assoc., 50 (2010), 745.   Google Scholar

[8]

Centers for Disease Control and Prevention (CDC), Interim guidance for clinicians on identifying and caring for patients with swine-origin influenza A (H1N1) virus infection,, (2009)., (2009).   Google Scholar

[9]

C. M. Chew and G. Eysenbach, Pandemics in the age of Twitter: Content analysis of tweets during the 2009 H1N1 outbreak,, PLoS One, 5 (2010).  doi: 10.1371/journal.pone.0014118.  Google Scholar

[10]

J. Cui, Y. Sun and H. Zhu, The impact of media on the control of infectious diseases,, J. Dyn. Differ. Equ., 20 (2008), 31.  doi: 10.1007/s10884-007-9075-0.  Google Scholar

[11]

A. Culotta, Towards detecting influenza epidemics by analyzing Twitter messages,, Proceedings of the First Workshop on Social Media Analytics, (2012), 115.  doi: 10.1145/1964858.1964874.  Google Scholar

[12]

D. Currie, Public health leaders using social media to convey emergencies: New tools a boon,, The Nation's Health, 39 (2009), 1.   Google Scholar

[13]

L. Donelle and R. G. Booth, Health tweets: an exploration of health promotion on twitter,, Online J. Issues Nurs., 17 (2012).  doi: 10.3912/OJIN.Vol17No03Man04.  Google Scholar

[14]

N. M. Ferguson, D. A. Cummings, S. Cauchemez, C. Fraser, S. Riley, A. Meeyai, S. Iamsirithaworn and D. S. Burke, Strategies for containing an emerging influenza pandemic in Southeast Asia,, Nature, 437 (2005), 209.  doi: 10.1038/nature04017.  Google Scholar

[15]

N. M. Ferguson, D. A. Cummings, C. Fraser, J. C. Cajka, P. C. Cooley and D. S. Burke, Strategies for mitigating an influenza pandemic,, Nature, 442 (2006), 448.  doi: 10.1038/nature04795.  Google Scholar

[16]

S. Funk, M. Salathe and V. A. Jansen, Modelling the influence of human behaviour on the spread of infectious diseases: A review,, J. R. Soc. Interface, 7 (2010), 1247.  doi: 10.1098/rsif.2010.0142.  Google Scholar

[17]

S. Funk, E. Gilad, C. Watkins and V. A. Jansen, The spread of awareness and its impact on epidemic outbreaks,, PNAS, 106 (2009), 6872.  doi: 10.1073/pnas.0810762106.  Google Scholar

[18]

J. Ginsberg, M. H. Mohebbi, R. S. Patel, L. Brammer, M. S. Smolinski and L. Brilliant, Detecting influenza epidemics using search engine query data,, Nature, 457 (2009), 1012.  doi: 10.1038/nature07634.  Google Scholar

[19]

M. Z. Gojovic, B. Sander, D. Fisman, M. D. Krahn and C. T. Bauch, Modelling mitigation strategies for pandemic (H1N1) 2009,, CMAJ, 181 (2009), 673.  doi: 10.1503/cmaj.091641.  Google Scholar

[20]

M. E. Halloran, N. M. Ferguson, S. Eubank, I. M. Longini, Jr., D. A. Cummings, B. Lewis, S. Xu, C. Fraser, A. Vullikanti, T. C. Germann, D. Wagener, R. Beckman, K. Kadau, C. Barrett, C. A. Macken, D. S. Burke and P. Cooley, Modeling targeted layered containment of an influenza pandemic in the United States,, PNAS, 105 (2008), 4639.  doi: 10.1073/pnas.0706849105.  Google Scholar

[21]

N. Heaivilin, B. Gerbert, J. E. Page and J. L. Gibbs, Public health surveillance of dental pain via Twitter,, J. Dent. Res., 90 (2011), 1047.  doi: 10.1177/0022034511415273.  Google Scholar

[22]

H. Hirose and L. Wang, Prediction of infectious disease spread using Twitter: A case of influenza,, The Fifth International Symposium on Parallel Architectures, (2012), 100.  doi: 10.1109/PAAP.2012.23.  Google Scholar

[23]

C. Holt, Emerging technologies: Web 2.0,, Health Information Management Journal, 40 (2011), 33.   Google Scholar

[24]

A. Java, X. Song, T. Finin and B. Tseng, Why we Twitter: Understanding Microblogging Usage and Communities,, in Proceedings of the 9th WebKDD and 1st SNA-KDD 2007 Workshop on Web Mining and Social Network Analysis, (2007), 56.  doi: 10.1145/1348549.1348556.  Google Scholar

[25]

V. Lakshmikantham, S. Leela and A. A. Martynyuk, Stability Analysis of Nonlinear Systems,, Marcel Dekker, (1989).   Google Scholar

[26]

J. P. LaSalle, The Stability of Dynamical Systems,, Regional Conference Series in Applied Mathematics, (1976).   Google Scholar

[27]

B. Y. Lee, S. T. Brown, G. W. Korch, P. C. Cooley, R. K. Zimmerman, W. D. Wheaton, S. M. Zimmer, J. J. Grefenstette, R. R. Bailey, T. M. Assi and D. S. Burke, A computer simulation of vaccine prioritization, allocation, and rationing during the 2009 H1N1 influenza pandemic,, Vaccine, 28 (2010), 4875.  doi: 10.1016/j.vaccine.2010.05.002.  Google Scholar

[28]

S. Leekha, N. L. Zitterkopf, M. J. Espy, T. F. Smith, R. L. Thompson and P. Sampathkumar, Duration of influenza A virus shedding in hospitalized patients and implications for infection control,, Infect. Cont. Hosp. Ep., 28 (2007), 1071.  doi: 10.1086/520101.  Google Scholar

[29]

J. Li, D. Blakeley and R. J. Smith?, The failure of $R_0$,, Computational and Mathematical Methods in Medicine, (2011).  doi: 10.1155/2011/527610.  Google Scholar

[30]

R. Liu, J. Wu and H. Zhu, Media/psychological impact on multiple outbreaks of emerging infectious diseases,, Comput. Math. Methods Med., 8 (2007), 153.  doi: 10.1080/17486700701425870.  Google Scholar

[31]

Y. Liu and J. Cui, The impact of media coverage on the dynamics of infectious disease,, Int. J. Biomath., 1 (2008), 65.  doi: 10.1142/S1793524508000023.  Google Scholar

[32]

I. M. Longini, Jr., M. E. Halloran, A. Nizam and Y. Yang, Containing pandemic influenza with antiviral agents,, Am. J. of Epidemiol., 159 (2004), 623.  doi: 10.1093/aje/kwh092.  Google Scholar

[33]

P. Manfredi, P. D. Posta, A. d'Onofrio, E. Salinelli, F. Centrone, C. Meo and P. Poletti, Optimal vaccination choice, vaccination games, and rational exemption: An appraisal,, Vaccine, 28 (2009), 98.  doi: 10.1016/j.vaccine.2009.09.109.  Google Scholar

[34]

S. M. Tracht, S. Y. Del Valle and J. M. Hyman, Mathematical modeling of the effectiveness of facemasks in reducing the spread of novel influenza A (H1N1),, PLoS One, 5 (2011).  doi: 10.1371/journal.pone.0009018.  Google Scholar

[35]

S. Merler, M. Ajelli and C. Rizzo, Age-prioritized use of antivirals during an influenza pandemic,, BMC Infect. Dis., 9 (2009).  doi: 10.1186/1471-2334-9-117.  Google Scholar

[36]

A. Mitchell, T. Rosenstiel and L. Christian, What Facebook and Twitter mean for news,, Pew Research Center's Project for Excellence in Journalism, (2012).   Google Scholar

[37]

L. Odden, Top 10 uses of Twitter,, Online Marketing Blog, (2008).   Google Scholar

[38]

P. Poletti, M. Ajelli and S. Merler, Risk perception and effectiveness of uncoordinated behavioral responses in an emerging epidemic,, Math. Biosci., 238 (2012), 80.  doi: 10.1016/j.mbs.2012.04.003.  Google Scholar

[39]

P. Poletti, B. Caprile, M. Ajelli, A. Pugliese and S. Merler, Spontaneous behavioural changes in response to epidemics,, J. Theoret. Biol., 260 (2009), 31.  doi: 10.1016/j.jtbi.2009.04.029.  Google Scholar

[40]

T. C. Reluga, Game theory of social distancing in response to an epidemic,, PLoS Comput. Biol., 6 (2010).  doi: 10.1371/journal.pcbi.1000793.  Google Scholar

[41]

D. Scanfeld, V. Scanfeld and E. L. Larson, Dissemination of health information through social networks: Twitter and antibiotics,, Am. J. Infect. Control, 38 (2010), 182.  doi: 10.1016/j.ajic.2009.11.004.  Google Scholar

[42]

A. Signorini, A. M. Segre and P. M. Polgreen, The use of Twitter to track levels of disease activity and public concern in the U.S. during the influenza A H1N1 pandemic,, PLoS One, 6 (2011).  doi: 10.1371/journal.pone.0019467.  Google Scholar

[43]

A. Smith and J. Brenner, Twitter use 2012,, Pew Internet and American Life Project, (2012).   Google Scholar

[44]

J. M. Tchuenche, and C. T. Bauch, Dynamics of an infectious disease where media coverage influences transmission,, ISRN Biomathematics, 2012 (2012), 1.  doi: 10.5402/2012/581274.  Google Scholar

[45]

J. M. Tchuenche, N. Dube, C. P. Bhunu, R. J. Smith and C. T. Bauch, The impact of media coverage on the transmission dynamics of human influenza,, BMC Public Health, 11 (2011).   Google Scholar

[46]

V. Tweedle and R. J. Smith, A mathematical model of Bieber Fever: The most infectious disease of our time?,, in Understanding the Dynamics of Emerging and Re-Emerging Infectious Diseases Using Mathematical Models (eds. S. Mushayabasa and C. P. Bhunu), (2012), 157.   Google Scholar

[47]

S. J. Sullivan, A. G. Schneiders, C. W. Cheang, E. Kitto, H. Lee, J. Redhead, S. Ward, O. H. Ahmed and P. R. McCrory, 'What's happening?' A content analysis of concussion-related traffic on Twitter,, Brit. J. Sports Med., 46 (2012), 258.  doi: 10.1136/bjsm.2010.080341.  Google Scholar

[48]

M. Szomszor, P. Kostkova and E. de Quincey, Swineflu: Twitter predicts Swine Flu outbreak in 2009,, in Electronic Healthcare, (2010), 18.  doi: 10.1007/978-3-642-23635-8_3.  Google Scholar

[49]

UK Health Protection Agency (HPA), https://www.hpa.org.uk/,, 2010., ().   Google Scholar

[50]

P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,, Math. Biosci., 180 (2002), 29.  doi: 10.1016/S0025-5564(02)00108-6.  Google Scholar

[51]

J. van Dijck, Tracing Twitter: The rise of a microblogging platform,, Int. J. of Media Cultural Polit., 7 (2012), 333.  doi: 10.1386/macp.7.3.333_1.  Google Scholar

[52]

K. Vance, W. Howe and R. P. Dellavalle, Social Internet sites as a source of public health information,, Dermatol. Clin., 27 (2009), 133.  doi: 10.1016/j.det.2008.11.010.  Google Scholar

[53]

M. Wazny, Using viral marketing in campaigns supporting health promotion,, Proceedings of the 13th World Congress on Public Health, (2012).   Google Scholar

[54]

J. T. Wu, S. Riley, C. Fraser and G. M. Leung, Reducing the impact of the next influenza pandemic using household-based public health interventions,, PLoS Med., 3 (2006).  doi: 10.1371/journal.pmed.0030361.  Google Scholar

[1]

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